Simplify the following expression: $ n = \dfrac{2q}{q + 1} - 7 $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{q + 1}{q + 1}$ $ \dfrac{7}{1} \times \dfrac{q + 1}{q + 1} = \dfrac{7q + 7}{q + 1} $ Therefore $ n = \dfrac{2q}{q + 1} - \dfrac{7q + 7}{q + 1} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{2q - (7q + 7) }{q + 1} $ Distribute the negative sign: $n = \dfrac{2q - 7q - 7}{q + 1}$ $n = \dfrac{-5q - 7}{q + 1}$